4. (a) 100 people are given a standard antibiotic to treat an infection and another 100 are given a new antibiotic. In the first group, 90 people recover; in the second group, 85 people recover. Let p be the probability of recovery with the standard antibiotic and p2 be the probability of recovery with the new antibiotic. We are interested in estimating = p1 - p2. Here we treat all the patients as independent and identically distributed (i.i.d.) observations from the whole population. i. Provide an estimate, standard error and a 99% confidence interval for 0. ii. If we want to test Ho 0 = 0 against H:00, compute the corresponding p-value. iii. If we want to test Ho: 0 = 0 against H : 0 < 0, compute the corresponding p-value.